Wave transmission network



Feb. 12, 1935. 4 DARLINGTON 1,991,195

WAVE TRANSMISSION NETWORK Filed Oct. 31., 1931 2 Sheets-Sheetl R F/6./ E

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Feb. 12, 1935. s DARLINGTON 1,991,195

WAVE TRANSMI SS ION NETWORK Filed Oct. 51, 1 v 2 Sheets-Sheet 2 FIG. 6

z 3 E k L Y FREQUENCY FIG. 8

S. DARLING TON. 8V

' A TTORNEV PatentedFeb; 12, 1935 ,ZUNFTED STATES PATENT 7 H 1.991.195 W EIWSM RK-1" Sidney Darlington, New York, N. assignor to f Bell Telephone Laboratories,Incorporated,New T 7 York, N. Y., a corporation of New York nppii at onpcmtersn mar. n fs'iazse f 7 C lai ns. (01. 178,44;

I This invention" relates to "wave. transmission networks 1 and more" particularly to networks of 'Ithas for its principal object the economy of elements m ne: construction of wave filter netorks and the like.

Another object is to. facilitate the insertion of the fr'equen'cy selective typelsuch asbroad band frequency selective networks between impedances of unequal value. 1 Y I In their general form the networks of the invention comprise a pair of reactive impedances in combination with two equal resistances are ranged as a W heatstone bridge or latticenetwork the two resistancesforming one pair of opposing branches and the tworeactive impedances form ing the other pair. The networks have the prop erty that, when connected between a wave source and a load having certain specified impedances, the frequency variation of the phase and: the amplitude of the output current may be made to correspond, except fora constantattenuation loss, to that ofany of thewell-known broadban'dwavefilters, for example those of Campbell Patent 1,227,113,,issued May 22,1917. j I

The natureof the invention will be more fully understood from the following detailed description and from the accompanying drawings of which? Figs. land 2 are theoretical diagrams used in the explanation of the principles of the inventions 1 p.

Fig. 3 is a network of knownftypej Fig. 4 shows curves illustratingcharacteristics of the invention; i i i Fig. 5 is one example of a network of the invention related, to the knowninetwork ofFig. 3; I

Fig.6 showsadditional curves illustrating char acteristics of the invention; 1

Fig. '7 shows schematically another .embodi ment of-the invention; I

Fig. 8' represents a known prototype of Fig 7; and

Fig. 9 illustrates certain characteristicsof the networks of Figsfil and 8.. 3 A: symmetrical lattice which may beregarded as a general prototype of the networks of the invention is shown in schematic form in Fig. .1.

This network comprisesgtwo equal line impedances Z1, which may =be' of any characterj whatsoever; and two lattice impedances '22, likewise unrestricted.

source having an E. M. F. E, and to the other end is connected a resistance R representinga load;

To one end of the network is I i a connected a resistanceR in serieswith a wave 1 Fliter, by G.- A. CampbeIl BeH System Technical J ournal, volaL- No". 2, November1922,and its use inaw'avefilter networks being described inlUnited StatesiPatent; 1,600,290.1ssued September 21, 1926 to1W. TqMartin'. .Sinceitisgpossible, hy the proper-selection of l the; impedancesgto make this network equivalent "in. its transmission properties to. 'anyother symmetrical form terminal networkits .usea's aprototype orgasa standardofcomparison will enable the properties of the; networks of the invention to be more readily; apprehended.

. The general form of .the networks of. the inven tion which is shown schematically in Fig. 2, is that.

of a lattice fnetwork having twof line branches, 1 constituted byv resistances 1 R and two latticec value. transmission characteristics, of the networksare determined by the character o'fift he impedances Z5 and Z15 and b 'makingthese" refacterist'ic scan be obtained. i

Eorthe general symmetrical lattice shown, in Fig. 1 the; output currentfldenoted by It, for

circuit is given by the formula: v g i In the case bf the network shown i nIFig. 2, the

If now Zs is. made equal to Z1; and Zs EquationiQ) becomeszj. V

i i; e ifl t lezs L g ;ez1 R+z-2) whichj indi cats that underthe conditionssp'ecii fied the. output current off the network of Fig. 2

branches.havingimpedances 1Z3: and'Ztrespec v tively. The network is adapted to be connected between H resistive f impedances "of magnitudes at the inputend and aR at the output 'end, the factor abeing a simple-numeric unrestricted in will have the same frequency variation of phase and amplitude as that of Fig. 1, but will be diminished in amplitude in proportion to the constant factor If the quantity or. is made unity, that is if the lattice ofFig. 2 is connected betweenequal terminal impedances resistance R, Equation (3) becomes: I

"is absent to the power received when the network ispresent. The unit of loss is the decibel, the-loss in'decibels being equal to ten times the common logarithm of the power ratio. 7

From Equations (1) and (4) it follows that the insertion loss due to the network of Fig. 2 will be the equal to that of Fig. 1 when the impedances are related as described above, plus a fixed attenuation loss of about 6 decibels. The frequency selectivity and the'phase displacementof the output currents will be the same for both networks.

The form of Equations (2) and (3) indicates that thefrequency variation of the outputcurrent in the network of Fig. 2 is not affected by variation of the resistances of the terminal impedances so long as their product is equal to R The actual :value'of' the output current is modified in proportion to the factor a (1 a) but the variations with frequency retain the same proportionatevalues. .By virtue of this property the network may be designed to operate between impedances of unequal value without change of its selectivity.

The design formulae for broad-band filter networks in accordance with the invention follow readily from the foregoing equations and from the principles discussed above and from the wellknown design rules for lattice type filters employing reactive impedances only. The design of lattice type filters is described in the aforementioned United States Patent 1,600,290 of September 21, 1926 to W. T. Martin and also in United States Patent 1,828,454 to W. H. Bode, issued October 20, 1931. The procedure will be illustrated in connection with the design of the simple low-pass filter illustrated schematically in Fig. 5.

In Fig. 3 is shown a low-pass filter of the lattice' type, the line branches of which comprise simple inductances' L1. and the lattice branches series resonant impedances L2 C2. The determination of the pass-band and the cut-off frequency for this'filter is illustrated by the curves of Fig. 4 of which curve 1 represents the variation of the reactance of inductances L1 with frequency, and curve 2 the variation of the reactance of the resonant impedances L2 C2. -The theory of the lattice filter points out that a pass-band occurs in those frequency ranges where the line branch reactances are of opposite sign to the reactancesof the lattice branches and that an attenuation band occurs when the reactances are of like sign. For .the circuit of Fig.3 the cut-01f frequency evidently occurs at the resonance of L2 C2 and the pass-band'in the range from this point to zero. In Fig. ithe cut-off frequency is designated f0.

The characteristic impedance K of the filter of Fig. 3 is given by i which has the value at frequencies close to zero.

tion at the-terminal junctions, the terminal impedances R are usually given the value:

inductance of value C2R inparallel with a,ca-.

pacity of value L .R When R' has the value given by Equation; (6), the elements of the parallel combination have the Thefrequency variation of the reactance of the parallel resonant lattice branch is represented by curve 3 of Fig. 4, the anti-resonance occurring at the same frequency as the resonance of L2 and C2.and the reactance having opposite sign to that of curve 2 at all frequencies.-"It follows that for the general lattice networks of the invention as illustrated by Fig. 2 a pass-band will exist when the two lattice branches Z2 and Zb have reactancesof the same sign and an attenuation band will exist whenthereactances are of opposite sign. This is a converse of the rule defining the transmission bands of the whollyreactive network of Fig. 1. I

The insertion loss characteristics of the lowpass network of Fig. 5 and of its prototype Fig. 4 are illustrated by curves 5 and 6 respectively of Fig. 6 in which the over-all attenuation is plotted To avoid transmis- I sion irregularities in the pass-band due to reflecagainst frequency, the attenuation being mease ured in decibels. The form of the two curves is the same but curve 5 has a vertical displacement,

of 6 decibels which represents the constant loss corresponding to the factor, a-:-(1+a) The attenuation peaks above the transmission band correspond to the crossing of curves 1 and 2 of Fig. 4. Such peaks occur in characteristics'of the general lattice filters of Fig. 1 whenever Z1 and Z2 are equal and in the networks. of the invention whenever the product Z2 Zb of the impedances of the lattice branches is equal to R the product of the resistance branch impedances; This is clear from equation (2) which shows that the output current is zero under this condition.

A typical band-pass filter of the invention is illustrated in Fig. 7, the reactance prototype beand moor- ,1

ing :shbwh Fig, 8. this filter the lattice branches impedance Zb *compr ises an inductance Lb and a capacity Cb. m series and the other branch impedance Zscomprises two "parallel res- 'onant*combinationsLwCa and Lli cs' connected "in ser ies; "The frequency variation of the reac tance's-of these bra'nches are shown "in '9 in w'hichcu'rve "l represeirts the combination In; and

Cb and dotted curve 8 represents thecon'ibinaticn 1a,- #Ca, La, Ca; ail-n "order "that there may beasing'le pass-"band, the reactances of Za and Zb must have the same in a single 'frequency range; This requires that "the resonance titre "quency of ZbshaH-co'incide With that-of-Za. The

limits of the band are determined by the two anti-resonance frequencies fiand fr of Ira Ca and Ly cflrespectively. The prototype inetwork of *Fig. 8 comprises two -li-ne"'*branches Shaving simple series resonant combinations L1 C1 therein and two lattice branches each constituted "by two'resonant -'cornbi-nati'ons L2 C22 and L2", 02' "connected in"=parall'el. That the two networks may have similar insertion loss characteristics requires the following relationship between the elements;

The networks will then have similar characteristics when inserted between terminal impedances of resistance R. w

The reactances of the branches of the prototype filter are represented by curves '7 and 90f Fig. 8 which correspond respectively to the line branches and the lattice branches. Curve 9 has a variation inverse to that of curve 8.

Equations (8) enable the band filter design to be arrived at in termsof the coefficients of the prototype filter, which latter may be designed in accordance with known principles as described, for example, in the aforementioned Patent 1,828,454 to H. W. Bode. In following this procedure the value of the resistance R is chosen as that of'the terminal impedances which will give the best match with the characteristic impedance of the prototype filterthroughout the transmission band. The filter networks of the invention may, however, be designed without reference to the prototype networks in accordance with the following procedure.

From Equation (2) it follows that, if the two latticebranch impedances Za and Zb of the general network of Fig. 2 are made equal, the output current will be given by a E(Z-R) (1-5-61) R(Z-l-R) where Z is the common valueof Za and Zb. So long as Z isa pure reactance the output current given by Equation (9) will have a constant amplitude, the only change with frequency being a variation of its phase. If, now, the two impedances Za and Zb, in addition to having their resonance frequencies so assigned as to provide a transmission band in a desired frequency range, are proportioned also so that throughout the major part of this range they are substantially .ceduradhowever, is the following: Having as:

signed theresonance and anti-resonance frequencies in .terms of the bandlocation, the .irnpedances may-have arbitrary values assigned to their elements consistent with these frequencies. A plot of thelreactancesat various frequencies like that ofTFig. i9 will-show the extent and the, nature of the flisparityiof the reactances in the band and will indicateinwhatproportion the ordinates of one or the .o'therYof-th'e curvesshould be increased or decreased to .makefit match the other curve -inlan optimum manner. "'Therequired element values are then found'by increasing or decreasing the arbitrarily chosen inductances of oneof the impedances in the proportion indicated and changing the capacities in an inverse relation.

Having thus determined a set of impedance coefiicients which make the two impedances substantially equal throughout the assigned band, H

the network may be used between terminal impedances of any resistance values provided that the resistances of the line branches are made equal to the geometric means of the terminal resistances. The uniformity of the outputcurrent in the transmission band range will not bemuch affected by changes in the terminal impedances but considerable changes may result in the attenuation outside the hand, For given values of the terminal impedances, control of the attenuation,characteristicfioutside the band may be effected by increasing or decreasing the reactances of the lattice branches in the same ratio, their resonance frequencies being kept constant.

The foregoing examples of networks of the invention serve to illustrate their general characteristics and the manner of their design. It is clear from the principles set forth that the types are not limited to these examples but maycomprehend equivalents of allsymmetrical lattice networksincluding high-pass filters, phase correctorsor delay networks and attenuation equalizers. i

What is'claimed is: 1. A four-terminal wave transmission network comprising four-impedance branches arranged in lattice formation, two similarly disposed arms of the lattice being constituted by equal resistances and the othertwo branches being constituted by reactances, said reactances being of the samesign in a preassigned frequency range defining a transmission band and being of opposite sign at other frequencies. l 2. A network in accordance with claim 1 in which the said reactances have substantially equal values in the frequency range defining a transmission band. i l

3. A lattice network having an insertion loss characteristic when inserted between terminal impedances of resistance R equivalent except for a constant additional attenuation loss to that of a prototype symmetrical lattice network having branch impedances of values Z1 and Z2, re-

stituted by equal resistancesofvalue R and lattice branches having impedances of value Z1 and Z2 respectively.

4. In combination witha wave source and a load having resistance impedances, a four-terminalnetwork connected therebetween comprising four-impedance branches arranged in lattice formation, two similarly disposed branches of the lattice comprising equal resistances of value equal to the geometric mean of the resistances of said wave source and said load and the other two branches of the lattice being constituted by unlike reactances, said reactances being proportioned to have the same sign in a pr'eassigned 7 frequency range whereby substantially uniform transmission between said source and said load is obtained in said range and to have opposite signs at all other frequencies whereby currents of frequencies outside said preassigned range are subject to a high degree of attenuation.

5. A combination in accordance with claim 4 in 'whichthe reactance branches or the lattice network have impedances of substantially equal value throughout the preassigned frequency range of uniform attenuation.

6. A band-pass filter network comprising fourimpedance branches connected in lattice formation, two of said branches comprising equal resistances and being disposedsymmetrically in said network and the other two branches being constituted by resonant reactance combinations, the resonance frequencies of said reactances being so assigned that the reactances are of the same sign at all frequencies between two finite frequencies defining the limits of a transmission band and are of opposite sign at all other frequencies. a

7. A low-pass filter network comprising fourimpedance branches connected in lattice formation, two of said branches comprising equal resistances and. being symmetrically disposed in said network and the other two branches being constituted by reactances proportioned with respect to each other to have the same sign at all frequencies below a definite value and to have opposite signs at all higher frequencies. 

